uses of pascal's triangle

It was named after French mathematician Blaise Pascal. Some of my students are trying to find "practical uses" for Pascal's triangle. Pascal’s Triangle is a triangular array of numbers where each number on the “interior” of the triangle is the sum of the two numbers directly above it. One use of Pascal's Triangle is in its use with combinatoric questions, and in particular combinations. Practical Uses for Pascal's Triangle Date: 2/27/96 at 20:14:58 From: Andrew Cotton Subject: Help with Pascal's Triangle Hi, I teach 7th grade math. Expand Using Pascal's Triangle (x+3)^4. We have situations like this all of the time. The coefficients will correspond with line of the triangle. For instance, when we have a group of a certain size, let's say 10, and we're looking to pick some number, say 4, we can use Pascal's Triangle to find the number of ways we can pick unique groups of 4 (in this case it's 210). Suppose that we want to find the expansion of (a + b) 11. All I have been able to find has been related to probability. And one way to think about it is, it's a triangle where if you start it up here, at each level you're really counting the different ways that you can get to the different nodes. REAL LIFE with Pascal’s Triangle One real life situation that Pascal’s Triangle is used for is Probability, and combinations. We use the 5th row of Pascal’s triangle: 1 4 6 4 1 Then we have. The triangle was actually invented by the Indians and Chinese 350 years before Pascal's time. https://medium.com/i-math/top-10-secrets-of-pascals-triangle-6012ba9c5e23 It has a number of different uses throughout mathematics and statistics, but in the context of polynomials, specifically binomials, it is used for expanding binomials.. Properties of Pascal's triangle some secrets are yet unknown and are about to find. In this post, we explore seven of these properties. Pascal's triangle. Pascal's Triangle or Khayyam Triangle or Yang Hui's Triangle or Tartaglia's Triangle and its hidden number sequence and secrets. So if I … So Pascal's triangle-- so we'll start with a one at the top. Pascal's triangle is an array of numbers that represents a number pattern. Binomial Expansion Using Factorial Notation. How many different combinations can I make if I take out 2 marbles• The answer can be found in the 2nd place of row 5, which is 10. there are alot of information available to this topic. Pascal's Triangle can be displayed as such: The triangle can be used to calculate the coefficients of the expansion of by taking the exponent and adding . Application - Combination• Pascal’s triangle can also be used to find combinations:• If there are 5 marbles in a bag, 1 red, 1blue, 1 green, 1 yellow and 1 black. There are many interesting things about the Pascal’s triangle. For example, say you are at an ice cream shop and they have 5 different ice creams. 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